Ukrainian forces are withstanding "new and even tougher assaults" on Soledar, near the eastern city of Bakhmut that Russia has been trying to capture for months, according to President Volodymyr Zelensky.
"I thank all our soldiers who protect our Bakhmut... (and) all the fighters in Soledar, who are withstanding the new and even tougher assaults from the invaders!" Mr Zelensky said in his daily address.
The troops "won additional time and (preserved) forces for Ukraine", he added.
"Everything is completely destroyed... the whole land in Soledar is covered with corpses of the invaders and is scarred from the explosions," the Ukrainian leader said.
Earlier Ukrainian officials said Russia has launched a new "powerful assault" led by the Wagner contract militia on Soledar.
The officials described a difficult situation for forces repelling the attacks on the salt mining town and nearby fronts.
Soledar, in the industrial Donbas region, lies a few miles from Bakhmut, where troops from both sides have been taking heavy losses in some of the most intense trench warfare since Russia invaded Ukraine nearly 11 months ago.
Ukrainian forces repelled an earlier attempt to take the town but a large number of Wagner units quickly returned, deploying fresh tactics and more soldiers under heavy artillery cover, Ukrainian Deputy Defence Minister Hanna Malyar said on Telegram.
"The enemy literally step over the corpses of their own soldiers, using massed artillery, MLRS systems and mortars," Ms Malyar said, describing the attackers as drawn from Wagner's best reserves.
Russia's defence ministry did not mention either Soledar or Bakhmut in a regular media briefing, a day after facing criticism for an apparently false claim of a missile strike on a temporary Ukrainian barracks.
Wagner, founded by Yevgeny Prigozhin, an ally of Russian President Vladimir Putin and also active in conflicts in Africa, has taken a prominent role in Russia's war effort in Ukraine.
Mr Prigozhin has been trying to capture Bakhmut and Soledar for months at the cost of many lives on both sides.
He said on Saturday its significance lay in a network of cavernous mining tunnels below the ground: "It not only (has the ability to hold) a big group of people at a depth of 80-100 metres, but tanks and infantry fighting vehicles can also move about."
President Volodymyr Zelensky said in nightly video remarks that Bakhmut and Soledar were holding on despite widespread destruction, but that in Soledar "things are very difficult".
Military analysts say the strategic military benefit for Moscow of capturing the towns would be limited.
A US official has said Mr Prigozhin is eyeing the salt and gypsum from the mines, believed to extend over 100 miles underground and contain auditorium-scale caverns.
In an evacuee centre in nearby Kramatorsk, Olha, 60, said she had fled Soledar after moving from apartment to apartment as each was destroyed in tank battles.
"All of last week we couldn't go outside. Everyone was running around, soldiers with automatic weapons, screaming," said Olha, who gave only her first name.
"There isn't one house left intact," she said. "Apartments were burning, breaking in half."
Pro-Russian bloggers quoted Mr Prigozhin as saying his forces were fighting for the administration building in Soledar.
The Ukrainian military said reinforcements had been sent to Soledar.
"There are brutal and bloody battles there - 106 shellings in one day," Serhiy Cherevatyi, a spokesman for the military in the east, said on Ukrainian television.
Read more:
Latest Ukraine stories
Some 40km to the north in the town of Siversk, Ukrainian soldier Heorhil, 28, said each side was hitting the other with heavy artillery. Russian regular forces had replaced less well-trained fighters in the area, he said.
"Unfortunately, both sides are suffering big losses, which means also our units have losses," he said, speaking near destroyed houses blanketed in snow. "One should never underestimate the enemy."
Reuters was not able to independently verify the battlefield reports.
Police looking for missing Britons
The British Foreign Office has said that two British men have gone missing in Ukraine.
The families of both the UK nationals are being supported, a statement said.
Ukrainian police said the men, aged 28 and 48, were doing voluntary work and were last seen on Friday heading to the town of Soledar, the BBC reported.
A Foreign, Commonwealth and Development Office (FCDO) spokesman said: "We are supporting the families of two British men who have gone missing in Ukraine."
Marketplace strike
Further north in the Kharkiv region, a Russian missile strike on a marketplace in the village of Shevchenkove killed two women and wounded four others, including a 10-year-old girl, regional prosecutors said.
Badly injured people lay on the ground and rescue workers sifted through piles of rubble, overturned and burning stalls, and a large crater, video footage from police and Ukraine's presidential office showed.
A police officer carried a girl with blood on her face from the scene.
Russia did not immediately comment on the reports from the village, which Kyiv recaptured from Moscow in September.
Ukrainian authorities reported Russian strikes on Ukraine's second city, Kharkiv, and infrastructure in the regions of Donetsk, Mykolaiv and Kherson.
As the war grinds towards the one-year mark, Russia's military is under domestic pressure to deliver battlefield successes. Hawkish voices have sought escalation, after the loss of captured territory and high rates of death and injury.
Russia, which initially cited a need to rid Ukraine of nationalists, now says it is fighting a Western threat to its own existence.
Kyiv and its Western allies, which have imposed broad sanctions on Moscow and sent Ukraine weapons to defend itself, say the invasion was entirely unprovoked.
Britain is considering supplying Ukraine with tanks for the first time, Sky News reported, citing a Western source.
Britain's Ministry of Defence did not immediately respond to a request for comment.
France, Germany and the United States all pledged last week to send armoured fighting vehicles, fulfilling a long-standing Ukrainian request.
The Kremlin said the new weapons would "deepen the suffering of the Ukrainian people" but not affect the outcome of the conflict.
